lecture1110 - ME 563 Mechanical Vibrations Lecture #11...

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ME 563 Mechanical Vibrations Lecture #11 Single Degree of Freedom Free Response (Matlab)
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Free Response (Matlab) 1 When using Matlab to analyze the free response of a system, we can either: - Derive the analytical solution and program this solution into Matlab along with the parameters of the model. - Allow Matlab to numerically integrate the equation of motion to obtain the response. However, Matlab requires that we define the system before it will solve for the response solution. There are two options: - State variable model - Transfer function model
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State Variable Modeling 2 Consider the disc on an incline with no forcing function: This equation is of second order; however, integrators are generally written to solve first order equations. To convert this equation of motion to a first order equation, the system states are defined as follows: Then the equation of motion is rewritten as follows:
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First-Order Equations 3 This equation is one of the two state variable equations we need. If we start with one second order equation, then we
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lecture1110 - ME 563 Mechanical Vibrations Lecture #11...

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